Search

It is known that the longitudinal and transverse excitation modes can exist in the vicinity of a quantum critical point in the ordered phase of quantum magnetic systems. The total moment sum rule for such systems is derived on the basis of the extended spin-wave theory, where both longitudinal and transverse magnetic excitations are taken into account. The sum rule is resolved into elastic, one-magnon, and two-magnon components. The formulation is applicable to spin systems with the longitudinal mode, such as $S=1$ systems with single-ion anisotropy of easy-plane type and spin dimer systems. The result helps us analyze and understand measured data of inelastic neutron scattering., Comment: 16 pages, 10 figures

Motivated by the recent progress of high-frequency ultrasonic measurements, we propose a theory of magnetoacoustic resonance as a microscopic probe for quadrupole degrees of freedom hidden in magnetic materials. A local strain driven by an acoustic wave couples to electronic states of a magnetic ion through various quadrupole-strain couplings, and this provides a periodically time-dependent oscillating field. As a typical two-level system with the quadrupole, we consider a non-Kramers doublet and investigate single- and multiphonon-mediated transition processes on the basis of the Floquet theory. An analytic form of the transition probability is derived within the weak coupling theory, which helps us analyze the magnetoacoustic quadrupole resonance. We apply the theory to realistic non-Kramers doublet systems for the f2 configuration in Oh and D4h symmetries, and discuss how to identify the relevant quadrupole by controlling the quadrupole-strain coupling with an applied magnetic field in ultrasonic measurements., 13 pages, 5 figures

Magnetic field-induced nonreciprocal magnon in noncollinear magnet is investigated in detail from symmetry viewpoint. To understand the nonreciprocal dispersion relation, we discuss similarity to t...

Motivated by the recent progress of phonon-mediated control in quantum spin devices, we propose a possibility of hybrid measurement using electron paramagnetic resonance (EPR) and a surface acoustic wave (SAW). Considering quadrupole-strain (QS) couplings suggested for silicon vacancies, we present a minimum model of the two-level system to investigate a magnetoacoustic resonance (MAR) coupled to various strain modes driven by the SAW. The longitudinal and transverse QS couplings can be changed by rotating a magnetic field, which depends on a combination of the strain modes. Using the Floquet theory, we elucidate each coupling effect on the time-averaged transition probability, especially focus on a single-phonon transition process. The important result is that the longitudinal QS coupling brings about a sharp photon-assisted resonance and leads to an abrupt change in the field-angle dependent transition probability. Since this phonon transition process is always accompanied by the photon transition, the field angle for the sharp resonance peak can be detected by the EPR measurement. The hybrid EPR-MAR measurement is useful to confirm the existence of quadrupole degrees of freedom strongly coupled to elastic strains, and thus it is expected to be a complementary probe for the precise evaluation of quadrupole properties., Comment: 10 pages, 12 figures

Crystal field triplet ground states in f2 configurations such as Pr ions have quadrupolar coupling as well as magnetic coupling to conduction electrons, leading to a nontrivial non-Fermi liquid Kon...

In PrOs4Sb12, the lowest-lying singlet and triplet states in a Pr 4f^2 configuration hybridize with conduction electrons having local a_u and t_u point-group symmetries. It is shown that for an attractive triplet pairing interaction, the orbital degrees of freedom of the t_u component are important. In addition, the Th point-group symmetry characteristic of skutterudites plays an important role in stabilizing triplet superconductivity., 4 pages, 2 figures

One possible origin of the field-induced ordered phase (FIOP) in PrOs 4 Sb 12 is an interaction of quadrupolar moments of Pr 4 f electrons in the singlet–triplet crystal-field (CF) levels. We study...

The Kondo effect in a $p_x + {\rm i} p_y$-wave superconductor is studied by applying the Wilson's numerical renormalization group method. In this type of superconductor with a full energy gap like a s-wave one, the ground state is always a spin doublet, while a local spin is shrunk by the Kondo effect. The calculated magnetic susceptibility indicates that the spin of the ground state is generated by the orbital effect of the $p_x + {\rm i} p_y$-wave Cooper pairs. The effect of spin polarization of the triplet superconductor is also discussed., 5 pages, 4 figures, to be published in J. Phys. Soc. Jpn

We study the local antisymmetric spin-orbit (ASO) coupling effect on spin, orbital, and charge degrees of freedom for the Kondo effect in a triangular triple quantum dot (TTQD). Here, one of the three QDs is coupled to a metallic lead through electron tunneling, and a local electric polarization is induced by the Kondo effect. The ASO interaction is introduced in the other two coupled QDs on the opposite side of the lead. Generally, the ASO coupling effect is very weak and not easily detectable, but it essentially causes spin and charge reconfigurations in the TTQD through the Kondo effect. Using an extended Anderson model for the TTQD Kondo system, we elucidate that the ASO coupling gives rise to a considerable reduction of the emergent electric polarization, as a consequence of the parity mixing of molecular orbitals in the triangular loop as well as the spin-up and spin-down coupling of local electrons. The latter leads to a local diamagnetic susceptibility owing to the ASO coupled spins. We also show that the Kondo-induced electric polarization can be controlled by the ASO coupling as well as by the magnetic flux penetrating through the TTQD., 11 pages, 5 figures

Spin-dependent electric dipole operators are investigated group-theoretically for the emergence of an electric dipole induced by a single spin or by two spins, where the spin dependences are completely classified up to the quadratic order. For a single spin, a product of spin operators behaves as an even-parity electric quadrupole operator, which differs from an odd-parity electric dipole. The lack of the inversion symmetry allows the even- and odd-parity mixing, which leads to the electric dipole described by the electric quadruple operators. Point-group tables are given for classification of the possible spin-dependent electric dipoles and for the qualitative analysis of multiferroic properties, such as an emergent electric dipole moment coexisting with a magnetic moment, electromagnon excitation, and directional dichroism. The results can be applied to a magnetic ion in crystals or embedded in molecules at a site without the inversion symmetry. In the presence of an inversion symmetry, the electric dipole does not appear for a single spin. This is not the case for the electric dipole induced by two spins with antisymmetric spin dependence, which is known as vector spin chirality, in the presence of the inversion center between the two spins. In the absence of the inversion center, symmetric spin-dependent electric dipoles are also relevant. The detailed analysis of various symmetries of two-spin states is applied to spin dimer systems and the related multiferroic properties., Comment: 28 pages, 9 figures

Orbital degrees of freedom of a Cooper pair play an important role in the unconventional superconductivity. To elucidate the orbital effect in the Kondo problem, we investigated a single magnetic impurity coupled to Cooper pairs with a $p_x +i p_y$ ($d_{x^2-y^2}+id_{xy}$) symmetry using the numerical renormalization group method. It is found that the ground state is always a spin doublet. The analytical solution for the strong coupling limit explicitly shows that the orbital dynamics of the Cooper pair generates the spin 1/2 of the ground state., Comment: 4 pages, 2 figures, JPSJ.sty, to be published in J. Phys. Soc. Jpn. 70 (2001) No. 10

The microscopic mechanism of circular currents induced in the vicinity of a non-magnetic impurity is analyzed for the (time-reversal symmetry breaking) chiral superconducting state ${\bf d}({\bf k}) = \hat{{\bf z}} (k_x \pm i k_y)$ which is very likely realized in Sr_2RuO_4. From the analytic, not self-consistent solution of the Bogolyubov-de Gennes equations we find two types of quasiparticle states, a bound state and the continuum state. Through impurity scattering the condensate transfers angular momentum to the quasiparticle states which generate a circular current. At low temperature the continuum part of the quasiparticle spectrum gives the main contribution. The non-selfconsistent solution yields a state of finite angular momentum. The comparison with the corresponding Ginzburg-Landau theory reveals the existence of a compensating counterflow created by the superconducting condensate. The currents and magnetic fields appearing around the impurity have possibly been observed by muon spin relaxation measurements., Comment: 16 page Latex, 3PS file, accepted by J.Phys.Soc.Jpn

In a previous paper a possibility of coexistence of two superconducting order parameters was discussed for the (1, 1, 0) surface of d x 2 - y 2 -wave superconductors. In the present report physical properties are examined particularly for the time-reversal-breaking state ( s ± i d ) near the (1, 1, 0) surface. The nature of coexisting order parameters shows up in the local density of states. It is also shown that the superconducting current flows along the surface due to the time reversal breaking and induces the magnetic field. The induced magnetic field can be used to detect the time-reversal-breaking states experimentally.

Magnetic excitation in a spin dimer system on a bilayer honeycomb lattice is investigated in the presence of a zigzag edge, where disordered and ordered phases can be controlled by a quantum phase transition. In analogy with the case of graphene with a zigzag edge, a flat edge magnon mode appears in the disordered phase. In an ordered phase, a finite magnetic moment generates a mean-field potential to the magnon. Since the potential is nonuniform on the edge and bulk sites, it affects the excitation, and the dispersion of the edge mode deviates from the flat shape. We investigate how the edge magnon mode evolves when the phase changes through the quantum phase transition and discuss the similarities to ordered spin systems on a monolayer honeycomb lattice., Comment: 17 pages, 13 figures

The boundary effect in d -wave superconductors is studied for specular and rough surfaces. In particular, the local density of states near the boundary is examined to see how the d -wave symmetry shows up in the direction dependence of the surface relative to the order parameter.

We study an orbitally degenerate Kondo effect in a triangular triple quantum dot (TTQD), where the three dots are connected vertically with a single metallic lead through electron tunneling. Both spin and orbital degrees of freedom play an important role in the SU(4) Kondo effect. This is demonstrated by an equilateral TTQD Kondo system at half-filling, by Wilson's numerical renormalization group method. We show how an emergent electric polarization of the TTQD is associated with a crossover from SU(4) to SU(2) symmetry in the low-temperature state. A marked sign reversal of the electric polarization is generated by the fine-tuning of Kondo coupling with degenerate orbitals, which can be utilized to reveal orbital dynamics in the SU(4) Kondo effect., 5 pages, 5 figures

A new type of Kondo effect in unconventional superconductors is studied theoretically by using the Wilson's numerical renormalization group method. In this case, orbital degrees of freedom of a Cooper pair play an important role. It produces multichannel exchange couplings with a magnetic impurity, although the impurity is just a local spin. Here we focus on a p x +i p y -wave state which is a fully gapped system. In this case, the ground state is always a spin doublet in all the T K /Δ region, and the local spin is shrunk by the Kondo effect in the strong coupling region ( T K /Δ→∞). Here T K and Δ are the Kondo temperature and the superconducting energy gap, respectively. It indicates that the spin of the ground state is generated by the orbital effect of the Cooper pairs. This is completely different from the s -wave pairing case where a Kondo singlet is stabilized for large T K /Δ values. This type of Kondo effect reflects the symmetry of the conduction electron system.

The Kondo effect strongly depends on spin and orbital degrees of freedom of Cooper pairs. We focus on the Kondo effect in a p x +i p y -wave superconductor with a full energy gap. The numerical renormalization study shows that the ground state is always a spin doublet for a S imp =1/2 local spin and that it is always a spin singlet for S imp =1. The latter is due to uniaxial spin anisotropy of the Cooper pair. We also compare these results with a case of the d x 2 - y 2 +i d x y -wave superconductivity having the same energy-gap structure.

Magnetic excitation in the interacting spin dimer system NH4CuCl3 is investigated on the basis of an extended spin-wave theory, assuming a doubled unit cell with four dimer sublattices of inequivalent intradimer interactions as suggested by neutron scattering measurements. In the magnetically ordered phase, there are both transverse (Nambu–Goldstone) and longitudinal (Higgs) excitation modes as in the pressure-induced ordered phase of the isostructural spin dimer compounds TlCuCl3 and KCuCl3. The inequivalent dimer model is consistent with the magnon dispersion relation at zero magnetic field and with the field dependence of the excitation energies obtained by neutron scattering and ESR measurements. This supports the existence of four dimer sublattices with inequivalent dimers in NH4CuCl3.

Electromagnon excitation is investigated on the basis of the symmetric spin-dependent electric polarization in both collinear and noncollinear magnetically ordered states. We focus on quantum spin systems with a large easy-plane single-ion anisotropy, where both massive longitudinal (Higgs) and massless transverse (Nambu–Goldstone) modes exist in the magnetic excitations. In the one-magnon excitation, it is found that the symmetric spin-dependent electric polarization is connected with the longitudinal fluctuation of the ordered moment and that the Higgs mode appears as the electromagnon excitation in collinear states. In noncollinear states, both the Higgs and Nambu–Goldstone modes are observable as the electromagnon excitation.

A magnetic flux effect is studied theoretically on an electric polarization induced by the Kondo effect in a triangular triple-quantum-dot system, where one of the three dots is connected to a metallic lead. This electric polarization exhibits an Aharonov–Bohm oscillation as a function of the magnetic flux penetrating through the triangular loop. The numerical renormalization group analysis reveals how the oscillation pattern depends on the Kondo coupling of a local spin with lead electrons, which is sensitive to the point contact with the lead. It provides an experimental implication that the Kondo effect is the origin of the emergent electric polarization.

In integer spin systems with a strong easy-plane type single-ion anisotropy, a paramagnetic ground state is stabilized with a finite excitation gap. Applying a magnetic field or pressure can collapse the excitation gap and induce quantum phase transition into a magnetically ordered state. In a lattice without the inversion symmetry at the magnetic ion site, electric polarization emerges spontaneously by the quantum phase transition. We study how excitation modes evolve with field or pressure and analyze the dynamical correlation functions of the electric polarization. In the case of the pressure-induced order, a longitudinal mode exists in the low-energy region in the vicinity of the quantum critical point. It corresponds to a “Higgs mode” and is observable as an “electromagnon” that is excited by the electric field component of light absorption.

The Kondo effect plays an important role in the emergence of electric polarization in a triangular triple-quantum-dot system, where one of the three dots is connected to a metallic lead through a point contact. The interplay between spin and charge distributions is investigated on the basis of an impurity Anderson model where the impurity-site cluster is described by a three-site Hubbard model. The numerical renormalization group analysis demonstrates that an applied magnetic field suppresses the Kondo effect and that the three-site spin correlations lead to an abrupt change in the local electric and magnetic polarizations. The controllability of this multiferroic behavior on the nanoscale is also discussed.

It was previously suggested that an odd-frequency pair amplitude exists in the vicinity of boundaries in unconventional superconductors. We develop this idea and quest for a novel superconducting order parameter with an odd-frequency dependence. For this purpose, we focus on p-wave superconductors and extend the quasi-classical theory to include the odd-frequency dependence in the order parameter. Both of the frequency and spacial dependences of the order parameter are determined self-consistently. Under a finite electron-phonon interaction, it is found that an odd-frequency order parameter is stabilized near the boundary and coexists with the even-frequency one. By analyzing the induced odd-frequency pair amplitude in terms of the superconducting quasi-particle wavefunction, it is found that the mid-gap bound state generates the emergent odd-frequency order parameter., Comment: 15 pages, 10 figures

Magnetic property of interacting spin trimer systems is studied theoretically focussing on (C 5 H 11 NO 2 ) 2 ·3CuCl 2 ·2H 2 O as a typical example, where the trimer is composed of three S =1/2 spins. It is reported that (C 5 H 11 NO 2 ) 2 ·3CuCl 2 ·2H 2 O has low-field and high-field magnetically ordered phases at low temperatures, where the two phases are separated by a 1/3 magnetization plateau region. The quantum phase transition and magnetic excitation are investigated on the basis of an extended spin-wave theory which was developed in studying interacting spin dimer systems. Formulation of dynamical spin correlation function is presented by introducing form factors for trimers with which interference effects inside the trimer can be taken into account appropriately. Introducing the form factors enables us to treat a trimer as a kind of an atom and makes the formulation simple. Magnetic excitations are classified with transverse and longitudinal modes. It is found that each mode is characterized by i...

Magnetic excitation in strongly coupled spin monomer and dimer system is studied theoretically focusing on Cu 3 Mo 2 O 9 as an typical example, where Cu 3 Mo 2 O 9 shows an antiferromagnetic long-range order at zero field. Introducing formfactors of dimers, we present the formulation for magnetic excitations. Under an external magnetic field, an additional field-induced quantum phase transition takes place due to the stabilization of a triplet state of the dimer. The recent experimental study revealed that Cu 3 Mo 2 O 9 shows an multiferroic behavior with an electric polarization in the magnetically ordered state. According to the field-induced transition, we find that the electric polarization should change drastically.

Roles of multipole degrees of freedom in multiband superconductors are investigated in a case of impurities whose low-lying states consist of singlet ground and triplet excited states, which is related to the experimental fact that the transition temperature $T_{\rm c}$ is increased by Pr substitution for La in LaOs$_4$Sb$_{12}$. The most important contribution to the $T_{\rm c}$ increase comes from the inelastic interband scattering of electrons coupled to quadrupole or octupole moments of impurities. It is found that a magnetic field modifies an effective pairing interaction and the scattering anisotropy appears in the field-orientation dependence of the upper critical field $H_{{\rm c}2}$ in the vicinity of $T_{\rm c}$, although a uniaxial anisotropic field is required for experimental detection. This would be proof that the Pr internal degrees of freedom are relevant to the stability of superconductivity in (La$_{1-x}$Pr$_x$)Os$_4$Sb$_{12}$., Comment: 10 pages, 5 figures, to appear in J. Phys. Soc. Jpn

We study inelastic impurity scattering effects in multiband superconductors, taking into account the experimental result that the transition temperature T c is enhanced by Pr substitution for La in LaOs 4 Sb 12 . We find that the possible T c enhancement is caused by the interband magnetic scattering intensified by the local multiorbital exchange scattering within the Pr low-lying singlet and triplet states. We also examine the magnetic field dependence of T c that reflects the local symmetry.

Magnetic excitation in coupled multispin system is studied theoretically focusing on Cu 2 Fe 2 Ge 4 O 13 and Cu 2 CdB 2 O 6 as typical examples of such system. These compounds consist of spin dimer and spin monomer parts and show an antiferromagnetic phase transition at low temperatures due to the spin monomer part. A multispin containing a spin dimer and spin monomers is treated as a basis unit. The multispin forms a spin multiplet and its energy levels are separated into high and low regions reflecting the characteristic energies of the dimer and monomer parts. We regard the system as interacting multispins and apply an extended Holstein–Primakoff theory by introducing bosons for each energy level of a spin multiplet. In the low-energy region, the obtained magnon dispersion and dynamical spin correlation function agree quantitatively with experimental results of inelastic neutron scattering performed in Cu 2 Fe 2 Ge 4 O 13 . Analyzing dynamical spin correlation functions, we find several high-energy mod...

Field-oriented anisotropy of specific heat and magnetization in PrOs 4 Sb 12 is discussed on the basis of the generalized Holstein–Primakoff formalism under magnetic fields. With a moderate amount of the mixing parameter characterizing T h symmetry, we obtain distinct anisotropy of the specific heat due to fluctuations for H ∥[100] and H ∥[110] both in the para and the antiferro-quadrupole phases. Tendency of the anisotropy in the specific heat is consistent with the experimental results, while the calculated anisotropy of the magnetization in the para phase is opposite to that observed in the experiment. Although the magnetic field usually suppresses fluctuations due to level splitting, the presence of the critical soft modes in the exciton dispersion contributes significantly to thermodynamic quantities in antiferro-quadrupole systems.

We study magnetic excitations for anisotropic spin dimer systems. We present a theory that describes not only the lowest-lying excitation mode but also higher-lying modes of the spin dimers, where the latter modes are important for quantum phase transitions driven by magnetic field and pressure in spin-gapped systems. As the most intriguing application, we calculate electron spin resonance (ESR) intensity in the presence of Dzyaloshinskii–Moriya (DM) interaction, which couples the local triplet with the singlet states of the dimer. The ESR intensities under various configurations of the DM interactions are reported in both disordered and field-induced ordered phases, which are very useful for the analysis of high-field ESR data.

One-magnon Raman scattering for interacting spin dimer systems is studied theoretically based on exchange light scattering process. We focus on a pressure-induced ordered phase, where a longitudinal excitation mode exists. We find that the Raman scattering probes the longitudinal mode selectively. The Raman intensity is finite only in the ordered phase and develops with pressure. We apply the theory to spin gapped systems such as TlCuCl 3 and NiCl 2 –4SC(NH 2 ) 2 to demonstrate that the Raman scattering is a suitable probe for the longitudinal mode.

A longitudinal excitation mode is important in spin-wave theory for three-dimensional interacting integer spin systems with uniaxial anisotropy of easy plane type. There is a critical value of the ...

A new feature of Kondo effect due to an orbitally degenerate impurity is presented for a crystal-field singlet–triplet case in the f 2 configuration. There are two stable states at low temperatures: one is a Fermi-liquid dominated by the f 2 singlet; the other is a non-Fermi liquid stabilized by a quadrupolar type of exchange interaction between the f 2 triplet and conduction electrons. The numerical renormalization group analysis shows that the competition of both states strongly enhances a coupling of conduction electrons with a scalar type of hexadecapolar moment of the impurity state, indicating that the charge degrees of freedom is relevant for the multiorbital case. This result supports the superiority of high-rank multipoles in f -electron systems such as the Pr-based filled skutterudite compounds.

A possibility of exciton-mediated mechanism is studied to describe the superconductivity in a Pr skutterudite PrOs 4 Sb 12 . In this compound the low-lying crystal-field states of Pr form a pseudo-quartet consisting of Γ 1 singlet ground and Γ 4 (2) triplet excited states. The dispersive crystal-field excitations (excitons) have been detected experimentally. The conduction electrons couple both magnetically and nonmagnetically with the pseudo-quartet. Believing that this coupling should be crucial for various properties of PrOs 4 Sb 12 , we determine the effective interaction between conduction electrons and the Pr pseudo-quartet states. It turns out that the nature of exchange processes is related closely to a u and t u components of the conduction electrons that correspond to the molecular orbitals of an Sb 12 cage surrounding a Pr ion. By the second-order perturbation in the exchange coupling, Cooper pairing interactions are derived both for singlet and triplet superconductivities. First, they are clas...